Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance

JOURNAL OF MULTIVARIATE ANALYSIS

卷:143

Article

Chiani, Marco¹ 

[1] Univ Bologna, DEI, I-40136 Bologna, Italy

关键词: Roy's test;    Random matrices;    Multivariate analysis of variance (MANOVA);    Characteristic roots;    Largest eigenvalue;    Tracy-Widom distribution;    Wishart matrices;   

DOI  :  10.1016/j.jmva.2015.10.007

来源: Elsevier

【 摘 要 】

Let X, Y denote two independent real Gaussian p x m and p x n matrices with m, n >= p, each constituted by zero mean independent, identically distributed columns with common covariance. The Roy's largest root criterion, used in multivariate analysis of variance (MANOVA), is based on the statistic of the largest eigenvalue, Theta(1), of (A + B)B-1, where A = XXT and B = YYT are independent central Wishart matrices. We derive a new expression and efficient recursive formulas for the exact distribution of Theta(1). The expression can be easily calculated even for large parameters, eliminating the need of pre-calculated tables for the application of the Roy's test. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free